The Tropical Fruit Forum

Your peat sounds to wet I think they might rot.
If you have
#1 Add Vermiculite to soak up excess water
(dry sand with no salt or even larger (silica)
 pavers sand rinsed in bucket since in Florida )
 (or add perlite to create air )

(or if you do not have those add more peat and make sure the soil is not to wet


 If you squeeze the peat in bag , and water comes wringing out of it not good

I like to before starting seeds to soak for 24 hours in plain water (or even 48)
 I've used Hot water a lot actually (changing it when it cools to hot)

you can also add air to the bag to create humidity
honestly I'd rather use a terrarium (sealed shut, but let the seeds breath after sprouting leaves every week
(Annonaceae  species for instance  not bean let those breath more often at least for me, and same with persimmon)

(if yuo see little flying knat s
keep root maggots off people use boiled marigold tea  to kill the larvae (natural insecticide
(I forgot how to spell  name but it's spelled  pyrethrin)

I like what gone tropo says about seeds out doors
it is cold in Florida now though
(So I cannot comment on your species with personal experience  with the cold out doors in Florida , )

NOTE if using a humidity dome
That is a controlled environment
growing out doors , and that is different keep that in mind
Bad bacteria can grow fast in a humidity dome !!!!

Out doors changes things , and they could grow great, but
Inside keep in mind if you use out door soil screen out any large half chucks of half decayed wood.
This should prevent Hydrogen Sulfide 9or rotten egg smell anaerobic
 (no oxygen to seeds in bag, but keep in mind hydrogen sulfide acts different out doors with plants, (in nature)
 but inside controlled environment will suffocate seeds)

(,  NOTE half decayed wood in out door soil  is bad (in bag) except I do like pine bark bought in the store even if not fresh )
Also NOTE cherimoya here is expensive here I have had seeds in a bag a long while ,
but it should not be soaking they will rot .

you should at least for the time being Add something to soak up all the excess water
Better to have them grow slow then rot fast

So to over complicate things here  (never a bag idea to  get a dollar store spray bottle and just mist your medium )
you did say damp peat , but at least me personally if only peat is used I  want it some what crumply
(like the consistency of moist oreo cookies mist every now and again (best I can explain )
A little drawn out explanation , and should of made it simplified

Without seeing a picture of the damp peat it is hard to know if too wet though (sorry, but I'm taking caution)

I have a silly little experiment I'm conducting...with germinating illama seeds....

I've heard it's best to let them sit out for a few months before planting....I think around 6 months or more is recommended....

but i took some fresh seeds....and soaked them in Coca-Cola (Mexican) for about 14 hours....i made sure they were completely submerged, because they wanted to float.

after they soaked in the coke, I noticed there was a slight discoloration (brown stain) on some of the seeds....

after soaking, I immediately planted them.

It would be interesting if somehow the Coke's ingredients (mainly phosphoric acid) helped breakdown the seed coat, and increased germination rate.